1. QND measurement of photons Quantum Zeno Effect & Schrödingers Cat Julien BERNU YEP 2007

2. Historical Zeno Paradox

4. Quantum Zeno Effect TimePosition T P(right)

5. Quantum Zeno Effect TimeP(right)

6. R1R2 Classical source Our experimental setup QND measurement of the photon number

7. Coupling the cavity to a classical source Classical source The field gets a complex amplitude in phase space Complex phase space

8. Coupling the cavity to a classical source Time Mean photon number Quadratic start Zeno Effect ! Coherent field:

9. Experimental difficulties

10. Why 1 Hz precision? Effect of a frequency noise or sideband picks on the source or the cavity: random phase for injection pulses. Complex phase space

11. How? Source: Anritsu generator locked on a (very) good quartz locked on a commercial atomic clock Source: Anritsu generator locked on a (very) good quartz locked on a commercial atomic clock Cavity: position of the mirrors must be stable at the range of 10 -13 m (10 -3 atomic radius)! Cavity: position of the mirrors must be stable at the range of 10 -13 m (10 -3 atomic radius)! Sensitivity to accoustic vibrations, pressure, temperature, voltage, hudge field… Sensitivity to accoustic vibrations, pressure, temperature, voltage, hudge field… V 4 He Recycling 0.1 mbar @ 1 bar 0.2 Hz 0.1 mV @ ~100V = 0.2 Hz P Pump Thermal contractions: (1kg) 100 µK @ 0.8 K 0.2 Hz

12. Results Injection watched with QND measurements: time Injection pulses (Zeno Effect) Measurement

13. Results Injection watched with QND measurements: time

14. Results Then with continuous measurement: Injection watched with QND measurements: Perfect control! to be removed… Zeno Effect!

15. Results

16. Results Perfect agreement!

17. QND detection of atoms Re( ) Im( ) a single atom controls the phase of the field R1R2

18. QND detection of atoms Re( ) Im( ) /2 pulse R 1 The field phase "points" on the atomic state R1R2 a single atom controls the phase of the field

19. This is a "Schrödinger cat state" on off 0 +1 on off 0 +1 Schrödingers Cat

21. Production of Schrödingers Cat by a simple photon number parity measurement ( phase shift per photon): Schrödingers Cat

22. Wigner Function (Phase space)

23. Wigner Function (Phase space)

24. Wigner Function

25. Statistical mixture

26. Wigner Function Schrödinger Cat

27. Wigner Function

28. Simple parity measurement !

29. Size of the cat

30. Observing the decoherence 2 200

31. Size of the cat

32. Atom chip experiment

33. Conclusion Using our QND measurement procedure, we have been able to prevent the building up of a coherent field by Quantum Zeno Effect. We can also use it to produce big Schrödinger cats and study their decoherence by measuring their Wigner function.

34. Perspectives 2 cavities for non-local experiments: teleportation of atoms teleportation of atoms non-local Scrödingers cat non-local Scrödingers cat quantum corrector codes quantum corrector codes

35. Thank you! The team: J. B. Samuel Deléglise Christine Guerlin Clément Sayrin Igor Dotsenko Michel Brune Jean-Michel Raimond Serge Haroche Sebastien Gleyzes Stefan Kuhr Atom chip team

37. The origin of decoherence: entanglement with the environment Decay of a coherent field: the cavity field remains coherent the cavity field remains coherent the leaking field has the same phase as the leaking field has the same phase as Environment

38. Decay of a "cat" state: cavity-environment entanglement: cavity-environment entanglement: the leaking field "broadcasts" phase information trace over the environment trace over the environment decoherence (=diagonal field reduced density matrix) as soon as: decoherence (=diagonal field reduced density matrix) as soon as: Environment The origin of decoherence: entanglement with the environment

39. Wigner functions of Schrödingers cats

40. Residual problem Dephasing per photon / Number of photons 02004006008001000 1.0 0.8 0.6 0.4 0.2 0

41. No quantum Zeno effect for thermal photons and decays

42. Zeno Effect for quadratic growth Time

43. Results: injection Effect of a small frequency detuning between the source and the cavity: Complex phase space

45. Quantum Zeno Effect

46. Graphes de wigner